Results 31 to 40 of about 1,956 (175)
A Multi-Dimensional Matrix Product—A Natural Tool for Parameterized Graph Algorithms
Algorithms, 2022 We introduce the concept of a k-dimensional matrix product D of k matrices A1,…,Ak of sizes n1×n,…,nk×n, respectively, where D[i1,…,ik] is equal to ∑ℓ=1nA1[i1,ℓ]×…×Ak[ik,ℓ].
Mirosław Kowaluk, Andrzej Lingas
doaj +1 more source
Fractional List Packing for Layered Graphs
Journal of Graph Theory, EarlyView.ABSTRACT The fractional list packing number χ ℓ • ( G ) ${\chi }_{\ell }^{\bullet }(G)$ of a graph G $G$ is a graph invariant that has recently arisen from the study of disjoint list‐colourings. It measures how large the lists of a list‐assignment L : V ( G ) → 2 N $L:V(G)\to {2}^{{\mathbb{N}}}$ need to be to ensure the existence of a “perfectly ...
Stijn Cambie, Wouter Cames van Batenburg
wiley +1 more source
An Algorithm for Subgraph Isomorphism
, 1976 Subgraph isomorphism can be determined by means of a brute-force tree-search enumeration procedure. In this paper a new algorithm is introduced that attains efficiency by inferentially eliminating successor nodes in the tree search.
J. R. Ullmann
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Efficient Algorithms for Subgraph Listing
Algorithms, 2014 Subgraph isomorphism is a fundamental problem in graph theory. In this paper we focus on listing subgraphs isomorphic to a given pattern graph. First, we look at the algorithm due to Chiba and Nishizeki for listing complete subgraphs of fixed size, and ...
Niklas Zechner, Andrzej Lingas
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A Coarse Geometric Approach to Graph Layout Problems
Journal of Graph Theory, EarlyView.ABSTRACT We define a range of new coarse geometric invariants based on various graph–theoretic measures of complexity for finite graphs, including treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these invariants can be used to define functions which satisfy a strong monotonicity property, namely, they are ...
Wanying Huang +3 more
wiley +1 more source
Defining Recursive Predicates in Graph Orders [PDF]
Logical Methods in Computer Science, 2018 We study the first order theory of structures over graphs i.e. structures of the form ($\mathcal{G},\tau$) where $\mathcal{G}$ is the set of all (isomorphism types of) finite undirected graphs and $\tau$ some vocabulary.
Ramanathan S. Thinniyam
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On a Clique‐Building Game of Erdős
Journal of Graph Theory, EarlyView.ABSTRACT The following game was introduced in a list of open problems from 1983 attributed to Erdős: two players take turns claiming edges of a Kn ${K}_{n}$ until all edges are exhausted. Player 1 wins the game if the largest clique that they claim at the end is strictly larger than the largest clique of their opponent; otherwise, Player 2 wins the ...
Alexandru Malekshahian, Sam Spiro
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Filtering for subgraph isomorphism
, 2007 A subgraph isomorphism problem consists in deciding if there exists a copy of a pattern graph in a target graph. We introduce in this paper a filtering algorithm dedicated to this problem.
Solnon, Christine +5 more
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Chromatic Ramsey Numbers and Two‐Color Turán Densities
Journal of Graph Theory, EarlyView.ABSTRACT Given a graph G, its 2‐color Turán number ex ( 2 ) ( n , G ) is the maximum number of edges in an n‐vertex graph, such that the edges can be colored with two colors avoiding a monochromatic copy of G. Let π ( 2 ) ( G ) = lim n → ∞ ex ( 2 ) ( n , G ) / n 2 be the 2‐color Turán density of G.
Maria Axenovich, Simon Gaa, Dingyuan Liu
wiley +1 more source
Testing first-order properties for subclasses of sparse graphs [PDF]
, 2013 We present a linear-time algorithm for deciding first-order (FO) properties in classes of graphs with bounded expansion, a notion recently introduced by Nešetřil and Ossona de Mendez.
Thomas, Robin +2 more
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